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Q.
The constant term in the expansion of $\left(2+5 x+a x^3\right)\left(\frac{3 x^2}{2}-\frac{1}{3 x}\right)^9$ is 1 . The value of a is
Binomial Theorem
Solution:
The term independent of $x$ is
$2 \cdot{ }^9 C _3\left(\frac{3}{2}\right)^3\left(\frac{-1}{3}\right)^6+ a \cdot{ }^9 C _2\left(\frac{3}{2}\right)^2\left(\frac{-1}{3}\right)^7=\frac{7}{9}-\frac{ a }{27}=1, $
$\text { giving } a =-6$